High-Activity Perturbation Expansion for the Hard Square Lattice Gas

TL;DR

This paper develops a high-activity perturbation expansion for the hard square lattice gas, providing an exact series expansion for the free energy near the high-density ordered phase.

Contribution

It introduces a systematic high-activity expansion and reorganization into a Mayer-like series for a polydisperse system of interacting rods, extending understanding of phase transitions in lattice gases.

Findings

Series summed to order 1/z^{3/2}

Reorganization yields a Mayer-like series

Provides insights into high-density phase behavior

Abstract

We study a system of particles with nearest and next-nearest-neighbour exclusion on the square lattice (hard squares). This system undergoes a transition from a fluid phase at low density to a columnar ordered phase at high density. We develop a systematic high-activity perturbation expansion for the free energy per site about a state with perfect columnar order. We show that the different terms of the series can be regrouped to get a Mayer-like series for a polydisperse system of interacting vertical rods in which the $n$-th term is of order $z^{-(n+1)/2}$, where $z$ is the fugacity associated with each particle. We sum this series to get the exact expansion to order $1/z^{3/2}$.